Local well-posedness for the Zakharov system in dimension $d=2, 3$

TL;DR

This paper proves local well-posedness of the Zakharov system in 2D and 3D for a broad range of initial data in the energy space, utilizing normal form reduction and Strichartz estimates.

Contribution

It extends the regularity range for local well-posedness of the Zakharov system, especially at the critical regularity where s=l-1.

Findings

Established local existence and uniqueness in energy space

Extended regularity range for initial data

Applied normal form reduction and Strichartz estimates

Abstract

The Zakharov system in dimension $d=2,3$ is shown to have a local unique solution for any initial values in the energy space $H^{s} \times H^{l} \times H^{l-1}$, where the range of regularity $(s, l)$ is extended, especially at $s=l-1$. The result is obtained mainly by the normal form reduction and the Strichartz estimates.